Patterns and Drivers of Deep Chlorophyll Maxima Structure in 100 Lakes: the Relative Importance of Light and Thermal Stratification

Home , Deep chlorophyll maximum, Epilimnion

LIMNOLOGY

and Limnol. Oceanogr. 63, 2018, 628–646 VC 2017 The Authors Limnology and Oceanography published by Wiley Periodicals, Inc. OCEANOGRAPHY on behalf of Association for the Sciences of Limnology and Oceanography doi: 10.1002/lno.10656

Patterns and drivers of deep chlorophyll maxima structure in 100 lakes: The relative importance of light and thermal stratification

Taylor H. Leach ,1,a* Beatrix E. Beisner ,2 Cayelan C. Carey ,3 Patricia Pernica,2 Kevin C. Rose ,4 Yannick Huot ,5 Jennifer A. Brentrup ,1 Isabelle Domaizon ,6 Hans-Peter Grossart ,7,8 Bastiaan W. Ibelings ,9 Stephan Jacquet,6 Patrick T. Kelly ,1 James A. Rusak ,10,11 Jason D. Stockwell,12 Dietmar Straile ,13 Piet Verburg 14 1Department of Biology, Miami University, Oxford, Ohio 2Department of Biological Sciences, University of Quebec at Montreal and Groupe de Recherche Interuniversitaire en Limnologie (GRIL), Montreal, Quebec, Canada 3Department of Biological Sciences, Virginia Tech, Blacksburg, Virginia 4Department of Biological Sciences, Rensselaer Polytechnic Institute, Troy, New York 5Departement de geomatique appliquee, University of Sherbrooke, Sherbrooke, Quebec, Canada 6INRA, UMR CARRTEL, Thonon les Bains cx, France 7Department Experimental Limnology, Leibniz Institute for Freshwater Ecology and Inland Fisheries, Stechlin, Germany 8Institute for Biochemistry and Biology, Potsdam University, Potsdam, Germany 9Institute F.-A.- Forel and Institute for Environmental Sciences, University of Geneva, Geneva, Switzerland 10Dorset Environmental Science Centre, Ontario Ministry of the Environment and Climate Change, Dorset, Ontario, Canada 11Department of Biology, Queen’s University, Kingston, Ontario, Canada 12Rubenstein Ecosystem Science Laboratory, University of Vermont, Burlington, Vermont 13Limnological Institute, University of Konstanz, Konstanz, Germany 14National Institute of Water and Atmospheric Research, Hamilton, New Zealand

Abstract The vertical distribution of chlorophyll in stratified lakes and reservoirs frequently exhibits a maximum peak deep in the water column, referred to as the deep chlorophyll maximum (DCM). DCMs are ecologically important hot spots of primary production and nutrient cycling, and their location can determine vertical habitat gradients for primary consumers. Consequently, the drivers of DCM structure regulate many characteristics of aquatic food webs and biogeochemistry. Previous studies have identified light and thermal stratification as important drivers of summer DCM depth, but their relative importance across a broad range of lakes is not well resolved. We analyzed profiles of chlorophyll fluorescence, temperature, and light during summer stratification from 100 lakes in the Global Lake Ecological Observatory Network (GLEON) and quantified two characteristics of DCM structure: depth and thickness. While DCMs do form in oligotrophic lakes, we found that they can also form in eutrophic to dystrophic lakes. Using a random forest algorithm, we assessed the relative importance of variables associated with light attenuation vs. thermal stratification for predicting DCM structure in lakes that spanned broad gradients of morphometry and transparency. Our analyses revealed that light attenuation was a more important predictor of DCM depth than thermal stratification and that DCMs deepen with increasing lake clarity. DCM thickness was best predicted by lake size with larger lakes having thicker DCMs. Additionally, our analysis demonstrates that the relative importance of light and thermal stratification on DCM structure is not uniform across a diversity of lake types.

*Correspondence: [email protected] aPresent address: Department of Biological Sciences, Rensselaer Polytechnic The vertical distribution of phytoplankton chlorophyll in Institute, Troy, New York lakes and oceans frequently exhibits a peak deep in the Additional Supporting Information may be found in the online version water column, referred to as the deep chlorophyll maximum of this article. or DCM (e.g., Fee 1976; Williamson et al. 1996a; Mignot This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in et al. 2011; Silsbe and Malkin 2016). DCMs can account for any medium, provided the original work is properly cited. as much as 60% of areal primary production in oligotrophic

628 Leach et al. Patterns and drivers of DCM structure across lakes lakes and oceans (Moll et al. 1984; Weston et al. 2005; reported as 1–3% of incident surface photosynthetically Giling et al. 2017) and influence nutrient cycling (Jamart active radiation (PAR; Fee 1976; Banse 1987, 2004; Perez et al. 1977; Letelier et al. 2004). DCMs create a vertical et al. 2002; Morel et al. 2007), or as daily integrated PAR val- resource gradient for primary consumers and thus influence ues of 0.1–1.2 mol quanta m22 d21 (Letelier et al. 2004; zooplankton vertical distributions and diel vertical migration Mignot et al. 2014). (Williamson et al. 1996a; Winder et al. 2003), as well as Other characteristics of DCM structure, aside from DCM predator aggregations (Tiselius et al. 1993). Additionally, depth, have received far less attention. Though analytical DCMs are often associated with elevated densities of mixo- definitions have varied, DCM thickness is generally defined trophic (Bird and Kalff 1989) and heterotrophic (Dolan and as the depth range over which a Chl peak occurs (Platt et al. Marrase 1995) protozoans, and bacterial biomass that can be 1988; Beckmann and Hense 2007; Hanson et al. 2007; Jobin 10X greater than elsewhere in the water column (Auer and and Beisner 2014). DCM thickness can be quantified as the Powell 2004). Consequently, the presence and characteristics depth range where Chl values are within a certain percent- of DCMs, such as their depth or size, can have important age of the maximum Chl concentration (e.g., Jobin and Beis- implications for predator–prey interactions, biogeochemistry, ner 2014), or where a certain percentage of the integrated and energy flow in aquatic ecosystems. Chl occurs (e.g., Platt et al. 1988). Although, when specifi- Many characteristics contribute to regulating the depth of cally considering deep biomass layers, the depth range of net DCM formation in lakes (Durham and Stocker 2012; Cullen primary production can also be used (Beckmann and Hense 2015). Light availability, the vertical distribution of 2007). nutrients, and the location of thermal gradients in the water The few studies that have examined factors controlling column are frequently identified as the main abiotic drivers DCM thickness have concluded that DCMs are thinner and of the depth of DCM formation (e.g., Fee 1976; Abbott et al. more sharply peaked with stronger stratification at the depth 1984). DCMs form because phytoplankton must balance at which they develop (i.e., where the relative availability of opposing gradients of light from above with the availability light vs. nutrients is optimized; Varela et al. 1994; Mellard of nutrients, which often increase with depth under strati- et al. 2011). In areas of strong stratification, non-motile cells fied conditions (Abbott et al. 1984; Carney et al. 1988; Clegg are hypothesized to aggregate in thin layers by sinking or ris- et al. 2007; Descy et al. 2010). Other biological factors can ing to the depths of neutral buoyancy (Alldredge et al. 2002; contribute to DCM formation, including high in situ growth Durham and Stocker 2012). Once these cells reach neutral at depth (Coon et al. 1987; Lande et al. 1989), or behavioral buoyancy, vertical dispersion is inhibited by the strong den- aggregations to nutrient-replete depths via physiological- sity gradient and in situ growth (Lande et al. 1989) and pho- influenced swimming in motile species (Durham and Stocker toacclimation (Fennel and Boss 2003) may further contribute 2012), or buoyancy-controlled movements in non-motile to high Chl concentrations over a small vertical depth range. species (e.g., Oliver 1994; Villareal et al. 1996). Horizontal Theoretical models predict that the exponential decay of movement of water masses such as intrusions or those that light in the water column, combined with a gradient of cause shear may also contribute to DCM formation by later- nutrient concentrations below the thermocline, means that ally transporting deep, nutrient- or phytoplankton-replete optimal conditions for high phytoplankton growth can exist waters (Durham and Stocker 2012). Under oligotrophic con- over an increasingly broad depth range with increasing lake ditions, DCMs may also form independently of phytoplank- transparency, which may also influence DCM thickness ton biomass peaks due to increased chlorophyll (Chl) per (Beckmann and Hense 2007). However, because our under- unit biomass because in these highly transparent lakes suffi- standing of mechanistic controls of DCM thickness primarily cient light may penetrate to depths with relatively higher stems from theoretical modeling (e.g., Varela et al. 1994; nutrient conditions, a process known as photoacclimation or Beckmann and Hense 2007; Mellard et al. 2011), not empiri- photoadaptation (Fennel and Boss 2003). These mechanisms cal studies (but see Mignot et al. 2011), the way in which are not mutually exclusive and may act in concert to con- these mechanisms interact across broad gradients of lake tribute to the formation of a DCM (Mignot et al. 2014). morphometry and transparency remains an open question. Thermal stratification determines DCM depth because it DCM features (i.e., depth and thickness) are likely con- can regulate nutrients mixing from deep waters into the trolled by simultaneously operating characteristics that co- euphotic zone (Abbott et al. 1984; Varela et al. 1994; Mellard vary with one another. Specifically, the strong co-variation et al. 2011; White and Matsumoto 2012) and is an important of light and temperature with depth (Houser 2006; Read and factor in determining the depth of strong vertical gradients Rose 2013) complicates our ability to differentiate the rela- in nutrients (i.e., the nutricline). Non-motile phytoplankton tive importance of each in controlling DCM structure. Both may also settle at depths of neutral density along a vertical light attenuation (Read and Rose 2013) and convective vs. temperature gradient (Alldredge et al. 2002; Durham and wind-driven mixing (Read et al. 2012) control the distribu- Stocker 2012). Accordingly, DCMs are frequently associated tion of incident thermal energy throughout the water col- with both the thermocline and areas of low light, often umn. As a result, both transparency and surface area may

629 Leach et al. Patterns and drivers of DCM structure across lakes interact to determine the strength and location of water col- to form (Durham and Stocker 2012 and references therein; umn stability, as well as the relative position of light and White and Matsumoto 2012). All data were collected during nutrient gradients. Moreover, lake surface area and depth mid-summer when surface water temperatures were the interact to influence transport processes such as mixing, sed- warmest in the water column and greater than 48C, which imentation, resuspension, and diffusion (Ha˚kanson 2005), are the requirements for thermal stratification (Boehrer and and thus may also modulate the influence of light and ther- Schultze 2008). While it is important to recognize that peaks mal stratification on DCM structure. in ChlF may not necessarily represent a biomass peak (Fen- A fundamental challenge in predicting DCM characteris- nel and Boss 2003), ChlF is a widely used proxy for phyto- tics and identifying the drivers of DCM structure in lakes has plankton biomass. One ChlF profile collected during the been a lack of data across broad gradients of lake transpar- mid-summer stratification was used for each lake. Although ency and morphometry. Most previous work, by necessity, this is a potential limitation due to temporal variability in has focused on DCM depth in one lake (Abbott et al. 1984), DCMs that have been observed in some lakes (Hamilton a small set of lakes through time (e.g., Hamilton et al. 2010), et al. 2010; Brentrup et al. 2016), we chose to focus here on or in a small set of lakes in a constrained geographical region cross-lake patterns in DCM characteristics, rather than sea- (Fee 1976; but see Longhi and Beisner 2009). These studies sonal dynamics, to maximize the number of available lakes have provided insight into the roles of lake trophy or clarity that had at least one ChlF vertical profile. on DCM depth. For example, DCMs deepen with increasing Chlorophyll fluorescence data processing water transparency (Fee 1976; Longhi and Beisner 2009; We classified lakes as having a DCM if a depth could be Hamilton et al. 2010). However, the relatively small number identified below the top 5% of the water column depth, of lakes limits our understanding of generalized patterns in where ChlF was at least 1.5 times the average fluorescence in DCM structure across broad gradients of lake size or transpar- the top 5% of the water column. Our DCM filter was fol- ency. Fortunately, recent advances in fluorometric sensors lowed by visual assessment of each profile to verify DCM and their widespread use have improved our ability to col- presence and to distinguish whether a lake had a single or lect information on the vertical distribution of Chl fluores- multiple peaks, resulting in a dataset of 100 lakes that exhib- cence across a large number of lake ecosystems (Brentrup ited a DCM. Although we could not compare lakes with and et al. 2016). without a DCM, these criteria allowed us to focus specifically We collated a 100-lake dataset of light, temperature, and on the drivers of variation in DCM structure within a popu- Chl fluorescence profiles collected during the summer strati- lation of lakes that exhibited DCMs. Note that while non- fied period from the Global Lake Ecological Observatory Net- photochemical quenching (NPQ) can reduce ChlF in high work (GLEON; Weathers et al. 2013; Rose et al. 2016) to light areas near the surface of lakes (Serra et al. 2009; Huot assess the relative importance of variables associated with and Babin 2010), we did not correct for NPQ because we are light availability vs. those associated with the depth and not aware of appropriate methods, given the diverse data strength of thermal stratification to predict DCM depth and and sensors used in our dataset. While NPQ may have thickness. Additionally, we assessed how light- and caused us to identify a lake as having a DCM when none stratification-associated variables scaled across broad gra- was present, this is unlikely because only three lakes fell dients of lake morphometry and transparency. To deal with close to our 1.5x fluorescence-depth threshold (1.5–1.6) for the analytical challenges of correlated explanatory variables DCM classification. The median ratio of average ChlF in the and non-linear relationships that often occur in large-scale top 5% of the water column to the ChlF at the DCM was 6 ecological studies, we used a random forest algorithm (Brei- (mean 5 10.9, 1st–3rd quartile 5 3.5–12.0, range 5 1.5–76.2). man 2001) to contrast the relative importance of predictors Further, Mignot et al. (2011) examined the effects of NPQ for the two focal DCM characteristics and to examine how on DCM depth and thickness in marine systems by compar- their importance varied across lakes. ing estimated Chl derived from in situ fluorescence vs. high performance liquid chromatography. The authors found that Methods NPQ caused an underestimation of DCM thickness in 24% Study sites of their dataset and that identification of the DCM depth In situ Chl fluorescence (ChlF) and temperature profiles was generally robust to NPQ. were collated from lakes representing 13 different ecological Fluorometer values were not comparable across lakes due regions in 8 countries (Abell et al. 2008, Fig. 1). The lakes to differences in the algorithm and calibration procedures spanned a broad range of lake size, maximum depth, trans- among different sensor models. We therefore normalized all parency, dissolved organic carbon concentrations, and tro- profiles to a maximum ChlF value of 100 within each lake to phic state (Table 1; Supporting Information Table S1). We facilitate comparisons among lakes. While normalization focused on thermally stratified temperate lakes during sum- meant that we could not compare the magnitude of the mer because the water column must be stratified for a DCM ChlF peak across lakes differences in ChlF values and ranges

630 Leach et al. Patterns and drivers of DCM structure across lakes

Fig. 1. Location of all 100 lakes included in the analysis. Insets are only for North America and Europe; lakes on other continents are shown on the world map. See Supporting Information Table S1 in the Supporting Information for more detailed information on each lake. Points in North American and Europe are semi-transparent so more darkly colored points represent overlapping points. between fluorometer manufactures would have made that (R Package pracma; Borchers 2015), which prevents local unfeasible even before the normalization. The depth inter- overshooting of data values, and thus preserved the shape of vals of the ChlF data within each lake were standardized to the ChlF profiles (Moler 2004). Prior to interpolation, the 0.1 m using a piecewise cubic hermite polynomial function median vertical resolution of the ChlF profiles across the

Table 1. Summary of characteristics for lakes in the dataset. Total phosphorus (TP), total nitrogen (TN), and dissolved organic carbon (DOC) represent epilimnetic concentrations. Note that TP and TN concentrations were not available for approximately one third of the study lakes.

Mean Median 1st–3rd quartile Range Sample size Surface area (km2) 37.97 0.44 0.17–1.43 0.004–1269 100 Max. depth (m) 44.5 20.6 12.7–38.8 4.3–501.0 91 TP (lgL21) 15.71 12.92 6.40–19.82 2.00–77.00 65 TN (mg L21) 0.34 0.29 0.22–0.41 0.03–1.12 63 DOC (mg L21) 4.07 3.45 1.45–5.73 0.18–24.40 91 1% PAR depth (m) 12.71 11.45 7.80–14.90 1.50–54.60 100

631 Leach et al. Patterns and drivers of DCM structure across lakes

occurred (Fig. 2). We fit a curve to each ChlF profile to characterize DCM thickness. Our approach built on previous studies that have characterized Chl profiles in a similar man- ner. Lewis et al. (1983) used a Gaussian distribution to represent vertical profiles of Chl a, and, Platt et al. (1988) and Morel and Berthon (1989) superimposed a Gaussian distribution onto a constant background Chl concentration. Recent studies have improved the curve fitting by superimposing the Gaussian profile onto a linearly (Uitz et al. 2006) or exponentially decreasing background Chl concentration (Mignot et al. 2011). We fit an exponential power distribution (Subbotin 1923), also known as a p-generalized normal distribution (Nadarajah 2006), with a constant background fluorescence to our ChlF profiles. The exponential power distribution is more flexible than a Gaussian distribution due to an additional shape parameter, which improved our characterization of the ChlF profiles. Our varied dataset prevented quantification of profile amplitude or magnitude however. For example, expressing the peak ChlF value as a quotient of the average or median ChlF in the profile was problematic because some of the profiles in the dataset did not cover the entire depth of the water column. Restricting the calculation of median or average ChlF values to within the euphotic zone (above the 1% PAR depth) did not provide an accurate or biologically relevant baseline ChlF estimate as the DCM extended below the 1% PAR depth in some lakes. We used an optimization procedure (R Developement Core Team 2015; function optim) to fit Eq. 1 to the normal- Fig. 2. (a) Diagram of the vertical distribution of chlorophyll fluores- ized and 0.1 m resolution ChlF profile in each lake. cence (ChlF) as defined by Eq. 1 where the background ChlF is repre- 0 1 sented by a, the mean of the exponential power distribution is p @ p 2jx2lj A represented by l, and the thickness is defined by 2r (i.e., 1r on either ChlFestimatedðÞx 5a1b e r (1) 1 side of l). (b) The shape parameter, p, controls the tail weight and thus 2rC p the shape of the profile (see “Methods” section for details), and profiles with several values of p and (r 5 3) are shown to demonstrate the vari- Equation 1 estimates ChlF at depth x (m), where a (unitless) ety of shapes that could be characterized with our curve-fitting proce- is an additive parameter that represents the background dure. (c–f) Example ChlF profiles (green) normalized to 100 and ChlF as implemented by Platt et al. (1988) and Morel and overlaid with the exponential power distribution (black). The solid point Berthon (1989). The multiplicative parameter, b (unitless), represents the depth of the ChlF maximum (ZDCM), which is the depth of the maximum ChlF value and the open circle represents, l. The thick- adjusts the amplitude of the DCM above the background ness of the deep chlorophyll maximum (DCM) is shown by the dashed ChlF. The remainder of the right-hand term in Eq. 1 is the gray lines and represents 1r on either side of l. Profile (c) is from Emer- exponential power distribution (R package pgnorm; Nadara- ald Lake (Wyoming, U.S.A.), ZDCM 5 14.1 m, l 5 14.9, r 5 3.29, jah 2005; Kalke and Richter 2013; Kalke 2015) where l (m) is p 5 3.300, profile (d) is from Heart Lake (Wyoming, U.S.A.) with the mean of the distribution. DCM thickness was defined as ZDCM 5 12.8 m, l 5 13.0, r 5 3.20, p 5 0.686, (e) is from Pincher Lake (Ontario, Canada), ZDCM 5 5.8 m, l 5 6.3, r 5 1.86, p 5 2.029 and (f)is the depth range that encompassed 1r (m) on either side of from Lake Truite (Quebec, Canada), ZDCM 5 4.3 m, l 5 4.4, r 5 0.99, l. The unitless shape parameter, p, controls the tail region p 5 0.661. The y-axes in (c–f) are consistent to improve comparisons and thus defines the shape of the distribution (Kalke and but note that the depths of the lakes differ. Richter 2013). When p 5 2, the curve is a Gaussian distribution, p < 2 indicate sharply peaked distributions and when entire dataset was 0.10 m (range: 0.01–0.65 m; 1st–3rd quan- p > 2 peaks are more broadly distributed (Fig. 2b, Nadarajah tile 5 0.05–0.10 m). 2005). C represents that gamma function. We calculated depth and thickness of the ChlF peak for Optimization was based on minimizing the total sum of each profile and used these as derived response variables in squares between the estimated ChlF values from the curve fit all analyses (Fig. 2). The depth of the DCM corresponded to and the normalized ChlF values for each profile. To provide the maximum ChlF observation in each lake. The thickness more ecologically meaningful descriptive metrics of the of the DCM was the depth range over which a ChlF peak DCM, constraints were placed on the exponential power

632 Leach et al. Patterns and drivers of DCM structure across lakes

distribution parameters including: 0 < l < maximum lake estimated Kd, as the slope of the linear regression of the nat- depth, r < one half of the maximum profile depth and a > - ural logarithm of downwelling planar irradiance (Ed) vs. 0.1. In cases where l-r was less than 0 (i.e., the fitted DCM depth. The regression was performed over the entire portion extended above the lake surface), we defined the top of the of the light profile that showed a visibly log-linear relation-

DCM as the lake surface. This scenario occurred only six ship between the ln(Ed(z)) vs. depth (Kirk 1994). In some times in our dataset and decreased the thickness of the DCM lakes, the depth range of the regression was altered to avoid an average of 3.3 m (median 5 1.9 m). When l1r extended boat shadows or surface waves that cause the light measure- below the maximum depth of the lake, the DCM bottom ments in the near surface to be particularly noisy. In the and thus the DCM thickness was not defined (five lakes were remaining 51 lakes, where radiometer data were unavailable, excluded because of this criterion). Kd was estimated by dividing 1.7 by the Secchi depth (Poole and Atkins 1929; Idso and Gilbert 1974). The depth at which Limnological data 1% of the surface PAR remained was estimated as: Based on mechanistic understanding of the factors that 5 = control DCM structure (e.g., Klausmeier and Litchman 2001; Z1% lnðÞ 100 Kd (2) Mellard et al. 2011; Durham and Stocker 2012; Cullen 2015), we selected a suite of predictors of DCM depth and thickness While light levels at the DCM are often reported as a percent associated with three categories: light attenuation, thermal of surface irradiance, daily-integrated light level (mols pho- stratification, and lake morphometry. Light attenuation vari- tons m22 d21) at a given depth is a better quantitative ables included the 1% PAR depth and epilimnetic dissolved descriptor of the amount of light at the DCM (Letelier et al. organic carbon (DOC) concentration because DOC is a major 2004; Mignot et al. 2014; Cullen 2015). However, in lakes regulator of light attenuation in aquatic ecosystems (Wil- where light attenuation (Kd) was estimated using a Secchi liamson et al. 1996b; Bukaveckas and Robbins-Forbes 2000). disk, irradiance measurements were not available. Because While DOC and light attenuation are closely related to one almost all study lakes were located in temperate latitudes another, we included DOC as a separate predictor in our where surface irradiance during summer is similar, our esti- model because recent ecological studies have shown that the mated 1% PAR depths are likely a reasonable proxy for com- effects of DOC on algal biomass can be positive at low DOC paring the amount of light available in the water column concentrations but negative at high DOC concentrations among lakes. (Seekell et al. 2015). Thus the role of DOC in predicting We estimated multiple metrics of thermal structure for DCM characteristics likely varies across lakes. Given the each lake in the dataset, including the depth of the thermo- importance of stratification for DCM formation (Cullen cline, the thickness of the metalimnion, buoyancy frequency 1982, 2015), we included several metrics related to the loca- at the thermocline, and the average buoyancy frequency in tion and strength of thermal density gradients in the water the DCM peak or within the metalimnion. Raw temperature column including the thermocline depth, thickness of the profile data were converted to 0.1 m resolution either by metalimnion, and the stratification strength (i.e., buoyancy averaging or linear interpolation, depending on the original frequency) at the thermocline and within the DCM (as data resolution. The only exception was for Lake Stechlin, defined by the depths of l6r). These metrics may predict Germany, where we interpolated the temperature data to the relative positions of light and nutrient gradients in the 0.5 m due to a low spatial sampling resolution (approxi- water column and thus the DCM structure. The strength of mately 1 m). From these temperature profiles, we estimated stratification at such depths may also be an important pre- the depth of the seasonal thermocline following procedures dictor of DCM thickness by influencing nutrient availability outlined in Read et al. (2011) using the rLakeAnalyzer pack- or the ability of cells to aggregate in the water column age (Winslow et al. 2016). To examine the effects of stratifi- (Klausmeier and Litchman 2001; Durham and Stocker 2012; cation strength, we also used the temperature profiles to Cullen 2015). Lake surface area and maximum depth were estimate profiles of buoyancy frequency (N) in each lake, also included in our analysis because they can influence which was defined as: transport processes in the water column (e.g., mixing, or sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi circulation-aided diffusion; Ha˚kanson 2005), and modulate g @p N5 2 (3) the influence of the light and thermal metrics on DCM p0 @z structure. Light, temperature, and DOC data for each lake were collected on the same day as the ChlF profiles except where g is the gravitational constant, p0 is the density at for Lake Champlain, where the Secchi measurement was each depth, and @p=@z is the density gradient (Kalff 2002). taken 4 d later. Density gradients were determined by applying finite center We determined the light attenuation coefficient of PAR, differencing to the density profiles, which were calculated 21 Kd (m ), for each lake in the dataset using two methods. using the 0.1 m resolution temperature data and thermody- For 49 of the lakes, radiometer data were available and we namic equations specific to freshwater conditions (Chen and

633 Leach et al. Patterns and drivers of DCM structure across lakes

Millero 1986). The top and bottom depths of the metalimn- A measure of importance was calculated for each predic- ion were defined as the depths above and below the thermo- tor by cross-validating each tree with data that were not cline where N reached at least 35% of the value of N at the used when the tree was constructed, referred to as the out- thermocline; these depths were found by moving away from of-bag data (Breiman 2001). For a given predictor variable the thermocline depth along the profile of N (Pernica et al. within a single tree, the out-of-bag values were randomly 2014) and were verified with visual inspection. Finally, from permuted and the mean square error (MSE) of the tree was the N profiles, we derived three additional metrics of thermal compared between the original out-of-bag and permuted stratification: (1) the value of N at the thermocline; (2) the out-of-bag datasets. A large percent increase in MSE from the mean buoyancy frequency within the DCM (determined by original out-of-bag data to the permuted out-of-bag data averaging all N values from the density profiles that indicated that the predictor variable had high explanatory fell between the top and bottom depths of the DCM peak, power for the response. Increase in percent MSE cannot be i.e., l6r, see above); and (3) the mean buoyancy frequency compared across RF with different response variables, so we within the metalimnion (determined by averaging all N val- calculated a relative increase in percent MSE (Rel. IMSE) for ues from the density profiles that fell within the each RF analysis by dividing the percent MSE for each vari- metalimnion). able by the highest observed percent MSE for a given Last, we collated several other limnological variables for response variable, following Read et al. (2015). each lake that may influence light attenuation or thermal We constructed a RF of 1500 trees for each of the two structure including, lake surface area and maximum depth response variables using 1% PAR depth (m), DOC concentra- 21 (both transformed using a logarithm base 10). Depth profiles tion (mg L ), thermocline depth (m), metalimnion thick- 21 and surface data of soluble or total nutrients were not avail- ness (m), buoyancy frequency at the thermocline (s ), lake 2 able for approximately one third of the lakes in our dataset. surface area (log10(km )), and maximum depth (log10(m)) as Thus, we did not include nutrients as predictors in our ran- predictors included in each analysis. For the RF analyses dom forest (RF) analyses because the lakes with nutrient data with DCM thickness as the response variables, only profiles 2 did not represent a random subsample of the entire dataset with a fitted R value 0.8 were used and buoyancy fre- 21 and were biased toward the low elevation and low transpar- quency within the DCM (s ) was included as an additional ency lakes. Results from a separate RF analysis of just the predictor variable. We also excluded six additional lakes lakes with nutrient data are included in the supplemental because the bottom depth of the DCM, as defined by the information (Supporting Information Fig. S4). curve fitting, extended below the bottom of those lakes. Because DCM thickness was derived from the curve fitting Random forest analysis procedures, our criteria ensured that only profiles where the We used a random forest (RF) algorithm to assess the rela- thickness was reasonably well characterized were used in the tive importance of predictors for each of the two DCM char- analysis (n 5 75 lakes total). All 100 lakes were included acteristics. RF analyses are robust to overfitting and when DCM depth was the response variable because it did insensitive to outliers (Breiman 2001) and are able to handle not use outputs from the curve fitting. For lakes where pre- datasets with relatively large numbers of candidate predic- dictor variables such as maximum depth or DOC concentra- tors. Importantly, RF analyses are able to detect non-linear tion were not available, the lake was excluded from that relationships without the need to specify them in advance individual tree, but not the entire analysis, following recom- (Jones and Linder 2015), accurately identify important pre- mendations from Liaw and Wiener (2002). Our data exclu- dictors of the response when there is high collinearity sion method affected 2.4% of the complete data matrix (700 among predictors (Archer and Kimes 2008), and provide observations) for the RF when DCM depth was the response accurate predictions of the response (Prasad et al. 2006; Cut- variable and 2.2% for the RF when DCM thickness was the ler et al. 2007). response (587 observations). A RF algorithm is a machine learning technique based on To visualize the direction and nature of the relationship classification, or in our case, regression tree analyses (Brei- between the most important predictors and each response, man 2001; Cutler et al. 2007). The RF algorithm builds and thus assess how the influence of each predictor scales many regression trees using a unique bootstrapped sample of across lakes, we constructed partial dependency plots (PDP) the data to construct each individual tree (Liaw and Wiener for the most important predictors from each RF model. Par- 2002). Results of each tree are combined to produce a tial dependence is computed by predicting the response model-averaged fit (Liaw and Wiener 2002). The method dif- (e.g., DCM depth or thickness) from the RF over a range of fers from traditional regression trees in that only a small values for the variable of interest, while holding all other number of randomly selected predictor variables are avail- variables in the dataset constant (Friedman 2001; also see able for selection at each node, which decreases the correla- Auret and Aldrich 2012 for an excellent description). In tion between trees and therefore the error rate of the entire essence, a PDP represents the relationship between a single forest (Archer and Kimes 2008). variable and the response, after accounting for the average

634 Leach et al. Patterns and drivers of DCM structure across lakes effects or interactions of the other predictors in the model Cryptophytes (cryptophytes and cyanobacteria containing (Carlisle et al. 2009). phycoerythrin). Browns were the dominant spectral group at All analyses were completed in R version 3.2.2 (R Devel- the depth of the DCM in a majority of the lakes (26 of 37 opement Core Team 2015) and the RF analyses were done lakes). Cryptophytes largely dominated the spectral composi- with an implementation written by Liaw and Wiener (2002; tion of the DCM in the remaining lakes (7 of 37), although R package randomForest). in one lake the DCM was evenly comprised of Browns and Cryptophytes. Cyanobacteria dominated the DCM in only Results three lakes and Greens were never the dominant spectral Cross-lake patterns in DCM characteristics group in the DCM (Supporting Information Fig. S3). We found a strong positive relationship between DCM Random forest analyses depth and thickness, and the 1% PAR depth (Fig. 3a,b), ther- Across all lakes, variables associated with light attenuation mocline depth (Fig. 3c,d), lake surface area (Fig. 3e,f) and (i.e., 1% PAR depth and DOC concentration) were more maximum lake depth (Supporting Information Fig. S1). The important than thermal stratification metrics to explain depth of the DCM ranged from 1.0 m to 53.9 m (mean 5 DCM depth (Fig. 5a). Together, all predictors in the RF 9.2 6 0.8 (1 SE), median 5 6.5; Table 2). In the 75 lakes model explained 63% of the variation in DCM depth. The where the ChlF distributions were well described by the 1% PAR depth was by far the most important variable curve-fitting procedure, DCM thickness ranged from 0.7 m explaining DCM depth, followed by DOC concentration, to 29.3 m (mean 5 6.8 6 0.8 (1 SE), median 5 4.3; Table 2). and the depth of the thermocline (Fig. 5a). The partial Eleven of the 100 lakes exhibited distinct double ChlF peaks dependency plots (PDP) showed that the predicted DCM in the profile, although no profile showed more than two depth increased rapidly with increasing 1% PAR depth until distinct peaks. Measured limnological variables did not differ the 1% PAR depth reached approximately 30 m, after which between lakes with a single vs. double peak. DCM depth and the response of the DCM depth to further increases in the thickness were also positively related to each other (Support- 1% PAR depth was weaker (Fig. 6a). There was a weak nega- ing Information Fig. S2). tive relationship between DOC concentration and the DCM The depth of the DCM was located at, or shallower than, depth at very low concentrations of DOC, and a stronger the 1% PAR depth in 87 of the 100 lakes (Fig. 4a). The negative relationship at intermediate DOC levels. At DOC median percent of incoming PAR that was available at the concentrations above 7–8 mg L21, further increases in DOC depth of the DCM across the entire dataset was 4.8%. With did not predict further decreases in DCM depth (Fig. 6b). one exception, the percent of PAR at the DCM was less than DCM depth increased with increasing depth of the thermo- 23% in all lakes (interquartile range 5 1.6–7.05%, min.–max. cline (Fig. 6c). 5 0.0001–52.9%). In the majority of the lakes, the depth of Lake surface area and maximum lake depth were the most the DCM was at or deeper than the top of the metalimnion important variables explaining DCM thickness, followed (85 lakes). Of that majority, 33 lakes had a DCM depth that closely by the depth of the thermocline (Fig. 5b). All predic- was located entirely below the metalimnetic layer (Fig. 4b). tors in the RF model explained 70% of the variation in DCM The 1% PAR depth was located below the top of the met- thickness. Predicted DCM thickness changed very little with alimnion in 99% of the lakes. In the one exception, Lake log-transformed lake surface area for lakes smaller than 2 Atitlan (Guatemala), the 1% PAR depth was located 2 m approximately 1 km , but showed a substantial increase in 2 above the estimated top of the metalimnion, although the thickness in lakes larger than approximately 10 km (Fig. DCM in Lake Atitlan was located below the 1% PAR depth. 7a). Similarly, predicted DCM thickness showed only moder- The 1% PAR depth was located below the thermocline in 96 ate increases when maximum lake depth was shallower than of the 100 lakes and below the bottom of the metalimnion 30 m, but a steeper positive relationship when maximum in 71 of the lakes (Fig. 4c). lake depth was greater than 30 m (Fig. 7b). The DCM also For a small and geographically biased subset of 37 lakes thickened with increasing thermocline depth, and this rela- (31 located in Quebec and Ontario, Canada, one in Virginia, tionship was strongest when the thermocline depth ranged U.S.A., five in western Europe), a spectrofluorometer (Fluo- from approximately 5–15 m (Fig. 7c,d). roprobe: bbe Moldaenke GmbH, Schwentinental, Germany) was used to collect ChlF. The spectrofluorometer parses the Discussion ChlF of four spectral groups of phytoplankton based upon Across a diverse and globally distributed set of lakes, we differences in accessory pigments and emission spectra (Beu- identified strong but markedly different patterns in the rela- tler et al. 2002). These spectral groups represent the follow- tive importance of light vs. thermal stratification in explaining broad taxonomic groupings: Browns (diatoms, ing DCM depth and thickness. Light and thermal dinoflagelletes, and chrysophytes), Greens (chlorophytes), stratification are important predictors of DCMs (e.g., Fee Cyanobacteria (phycocyanin containing cyanobacteria), and 1976; Cullen 1982, 2015). However, their strong covariation

635 Leach et al. Patterns and drivers of DCM structure across lakes

Fig. 3. Deep chlorophyll maximum depth and thickness as a function of 1% PAR depths (a, b), thermocline depth (c, d), and lake surface area (e, f). Black lines in (a, c) represent the 1 : 1 line. In (c) Lakes Tahoe and Taupo are shown in black for better visualization of the 1% PAR depths in the rest of the dataset. Tahoe and Taupo had 1% PAR depths of 54.6 m and 53.8 m, respectively. 636 Leach et al. Patterns and drivers of DCM structure across lakes

Table 2. Descriptive statistics of DCM depth and thickness (quantiﬁed in meters). See “Methods” section for complete deﬁnition of each characteristic, and Supporting Information Table S1 for complete information on all study lakes.

Mean (standard error) Median 1st–3rd quartile Range Sample size DCM depth (m) 9.2 (0.8) 6.5 4.3–11.0 1.0–53.9 100 DCM thickness (m)* 6.8 (0.8) 4.3 2.3–9.3 0.7–29.3 75 * Only lakes with R2 0.8 from the ChlF curve fitting procedure and for which the DCM bottom depths were defined above the bottom of the lake were included. had previously precluded a sufficient evaluation of their rela- depth of the nutricline increased relative to the 1% PAR tive importance and influence over the different elements of depth. Similarly, in a modeling study, Mellard et al. (2011) DCM structure within and across lake types. We found that demonstrated that when the depth of the nutricline was light attenuation and associated variables (e.g., DOC concen- held constant, DCM depths were sensitive to small decreases tration) were more important predictors of DCM depth than in light attenuation and thus to the relative position of the were predictors associated with thermal stratification. In con- 1% PAR and nutricline depths. Nutrient concentrations gen- trast, DCM thickness was predicted by lake size, maximum erally increase with increasing depth in a stratified water col- depth, and other limnological variables related to thermal umn (Holm-Hansen et al. 1976; Cullen 1982; Moll et al. stratification. Importantly, our analysis also suggests that the 1984) and likely play an important role in regulating DCM relative importance of light and thermal stratification on depths. While depth profiles of nutrient data were not avail- DCM structure is not uniform across broad gradients of lake able for all of the lakes in our dataset, these previous studies morphometry and transparency, but overall these abiotic strongly suggest the need to examine the role of vertical dis- characteristics explain a majority of the variation in DCM tribution of nutrient availability in future empirical studies. depth or thickness among lakes. However, we note that our RF model explained a substantial amount of variation in DCM depth among lakes in the DCM depth absence of nutrient predictors, indicating that physical char- The positive relationship that we observed between DCM acteristics alone can provide the ability to explain a majority and 1% PAR depths across a diverse set of lake types (Fig. 3a) (63%) of variation in DCM depth across lakes with diverse is consistent with results from previous studies, which characteristics. encompassed a narrower range of lake types (e.g., Fee 1976). DOC is a major regulator of water clarity and light attenu- The positive relationship has largely been attributed to phy- ation in aquatic ecosystems due to its light-absorbing proper- toplankton balancing the need for light from above and ties (Williamson et al. 1996b; Bukaveckas and Robbins- nutrients from hypolimnetic waters below to maximize Forbes 2000). Therefore, we were not surprised that DOC growth (Abbott et al. 1984; Durham and Stocker 2012), emerged as an important explanatory variable of DCM depth although photoacclimation also plays a role (Fennel and in our analysis. As with 1% PAR depth, the relationship Boss 2003). Our results, from a wider range of lake types, between predicted DCM depth and DOC concentration was also show that the relationship between 1% PAR and DCM not uniform across lakes (Fig. 6b), suggesting that the DOC depth is not uniform across a gradient of lake transparency concentration within a lake will alter the role that DOC (Fig. 6a). Predicted DCM depths from the RF analysis were plays in influencing DCM depth. Because the relationship more sensitive to increases in 1% PAR depth between depths between DOC concentration and the 1% PAR depth is char- of 10–30 m in the water column (Kd range: 0.46–0.19), but acterized by a negative power function, a unit increase in were less sensitive when 1% PAR was deeper than 30 m (Kd DOC reduces the 1% PAR depth much more in low DOC < 0.19). lakes compared to high DOC lakes (Morris et al. 1995). Sup- Differences in the relative position of the 1% PAR depth porting this “diminishing returns” concept, our results show and the nutricline may be responsible for the variability in that the predicted DCM depth became shallower with the relationship between DCM and 1% PAR depths across increasing DOC until approximately 7–8 mg L21, after which lakes observed in our dataset (Abbott et al. 1984; Barbiero continued increases in DOC had little influence on the pre- and McNair 1996). The relative positions of the 1% PAR and dicted DCM depth. Williamson et al. (1996b) identified a nutricline depths will alter the depth at which light avail- similar threshold in DOC concentration ( 8–9 mg L21), ability from above and nutrient availability from below are above which the influence of DOC in regulating the 1% PAR balanced and thus interact to control the DCM depth. For depth decreased substantially. example, Barbiero and McNair (1996) observed that the DCMs are often considered characteristic of highly trans- DCM in a small oligotrophic lake deepened over time as the parent, oligotrophic lakes (Fee 1976; Moll and Stoermer

637 Leach et al. Patterns and drivers of DCM structure across lakes

by two recent studies (Simmonds et al. 2015; Brentrup et al. 2016; Supporting Information Table S1). Previous studies also indicated that light must penetrate below the surface mixed layer for a DCM to form (e.g., Hamilton et al. 2010; Simmonds et al. 2015; Brentrup et al. 2016). Consistent with this, in all 100 lakes in our dataset, including the most eutrophic lakes (Trophic State Index, TSI > 50: Supporting Information Table S1), we observed that the 1% PAR depths extended below the thermocline. DCM thickness Our RF analysis found that larger and deeper lakes have thicker DCMs. Modeling studies predict that weak thermal stratification around the depth of the DCM will result in thicker Chl peaks (Mellard et al. 2011). The importance of lake size in predicting DCM thickness in our study is likely due to differences in stratification strength between large and small lakes. Lake surface area controls several aspects of thermal stratification and the location of density gradients in the water column (MacIntyre and Melack 2009). The controls of lake stratification reflect the balance of energy between solar radiation inputs that enhance stratification and wind and convective mixing, which serve to weaken stratification (MacIntyre and Melack 2009; Read et al. 2012). Larger lakes are less sheltered from the wind (Markfort et al. 2010) and have a longer fetch (Mazumder and Taylor 1994). Thus, larger lakes are subject to higher levels of wind-mixing and weaker stratification than smaller lakes (Rueda-Valdivia and Schladow 2009), creating conditions for a thicker DCM. Interestingly, our analysis also showed that the effect of lake surface area on predicted DCM thickness is stronger in lakes > 1km2, which is a similar size cutoff identified in previous studies that examined the importance of lake size on physical processes (1–10 km2; e.g., Hondzo and Stefan 1993; Read et al. 2012). Weaker stratification with increasing lake size may explain why lake size emerged as an important predictor of DCM thickness in our model. However, the mechanism remains unclear because buoyancy frequency within the DCM, a metric of thermal stratification strength, was not a particularly important predictor of DCM thickness in our RF analysis. Previous studies have found that the strength of Fig. 4. Frequency polygons of the ratios of (a) DCM depth to 1% PAR stratification around the depth of the DCM was negatively depth, (b) DCM depth, and (c) 1% PAR to metalimnion top, bottom, related to DCM thickness (Varela et al. 1992; Klausmeier and and thermocline depth for each lake in the dataset, respectively. Note that the x-axis scale differs among panels but that the bin size is 0.3 for Litchman 2001; Jobin and Beisner 2014). While our dataset all panels. In (b, c), a single lake is not shown that had DCM depth: showed exclusively narrow DCMs when buoyancy frequency thermocline and DCM depth: metalimnion bottom depth ratio of 44 within the DCM was high (i.e., when stratification was and a PAR: thermocline and PAR: metalimnion top value of 40. strong), our data showed highly variable DCM thickness in weakly stratified conditions (i.e., at low buoyancy fre- 1982). Our results, while supporting previous findings that quency). The high variability in DCM thickness when buoy- DCMs may be more common in oligotrophic lakes, show ancy frequency was low is likely the reason that buoyancy that they are not exclusive to these systems (Williamson frequency within the DCM does not appear as an important et al. 1996b). We found that DCMs can also be found in predictor of DCM thickness in our RF analysis. This high var- meso- to eutrophic and dystrophic lakes, as was also noted iability in DCM thickness under weakly stratified conditions

638 Leach et al. Patterns and drivers of DCM structure across lakes

Fig. 5. Relative increase in mean square error from the random forest regression for predicting DCM depth (a) and thickness (b). Higher values indicate higher importance of predictor variables. For analysis shown in (b), only 75 lakes where the ChlF curve fitting procedure yielded R2 0. 8 and where the DCM bottom depths were defined above the bottom of the lake were included. The DCM thickness was defined by 2r from the DCM depth (see “Methods” section for full details). Buoyancy frequency in the DCM represents the average buoyancy frequency within that depth range. Metalimnion is abbreviated as meta., buoyancy frequency as buoy. freq, and thermocline as thermo. The predictors in the random forest model (a) explained 63% of the variation in DCM depth and 64% of the variation in DCM thickness (b).

suggests that other factors unaccounted for in our study become a more important controller of DCM thickness with were likely affecting DCM thickness (e.g., behavioral aggre- increasing buoyancy frequency at the depth of the DCM gation, (Alldredge et al. 2002), zooplankton grazing, (Pilati (Fig. 8). and Wurtsbaugh 2003) or phytoplankton competition (Car- Maximum lake depth was also an important explanatory ney et al. 1988)) while thin DCMs observed under strongly variable of DCM thickness. It is likely that lake depth itself is stratiﬁed conditions suggests that stratiﬁcation strength may not a direct causal driver of DCM thickness. Rather, lake

639 Leach et al. Patterns and drivers of DCM structure across lakes depth and basin shape can influence and are correlated with example, maximum lake depth is negatively correlated with many other physical, chemical, and biological characteristics lake productivity (Carpenter 1983), and in a study of over of lakes (Ha˚kanson 2005; Johansson et al. 2007). For 1000 lakes in the United States, maximum lake depth was the most important explanatory variable of epilimnetic levels of total phosphorus, total nitrogen, turbidity, and DOC (Read et al. 2015). The exact mechanism behind maximum lake depth as an important predictor of DCM thickness in our study, and its role in other previous empirical studies, remains unclear. The influence of lake depth on transport processes such as mixing, sedimentation, resuspension, or diffusion (Ha˚kanson 2005), which influence vertical gradients in nutrients and light, and their relative vertical positions, may be important. In a coupled bio-physical process model, Ha˚kanson (2005) showed that when lake surface area is held constant, Secchi disk depths were deeper in a deep vs. a shallow lake. This occurred because the proportion of bottom sediment area that is susceptible to turbulent resuspension is lower in deeper lakes compared to shallower lakes, resulting in a greater flux of nutrients from the sediments to the water column in a shallower lake. The increased nutrient concentration due to this resuspension fueled an increase in epilimnetic primary production, and thus a decrease in Sec- chi disk depths in the shallower lake (Ha˚kanson 2005). Dif- ferences in maximum lake depth may also contribute to variation in the vertical distribution of thermal energy in the water columns of lakes, with important implications for DCM structure.

Phytoplankton community composition of the DCM The composition of the DCM from the spectroﬂuorometer data are consistent with previous lakes studies that have shown that DCMs are typically dominated by Browns (diatoms, dinoﬂagelletes, and chrysophytes) (Fee 1976; Abbott et al. 1984; Barbiero and Tuchman 2004; Saros et al. 2005; Hamilton et al. 2010; Simmonds et al. 2015), cryptophytes (Barbiero and Tuchman 2004; Camacho 2006), and less frequently cyanobacteria (Padisak et al. 2003; Camacho 2006). Browns, cryptophytes and cyanobacteria are hypothesized to dominate DCMs because they can maintain their vertical position in the water column either through active

Fig. 6. Partial dependency plots for the top three explanatory variables in the random forest model where DCM depth was the response variable; (a–c) are in descending order of importance. The partial dependency is the dependency of the predicted mean DCM depth, (the mean response) on each explanatory variable after averaging out the effects of all other predictors in the model. Tick marks along the x-axis represent the 10th–90th percentiles of each predictor, in 10 percentile increments, from the empirical dataset. Inset in (b) shows the full range of DOC concentrations in the dataset, while the main plot shows a subset of these data where the majority of empirical values exist for improved visualization of the relationship. Horizontal relationships indicate values of the explanatory variables where changes in the variable have little inﬂuence on the response after accounting for all other variables in the analysis.

640 Leach et al. Patterns and drivers of DCM structure across lakes

swimming or buoyancy regulation, show decreased settling rates under nutrient-replete and low light conditions (i.e., diatoms, Richardson and Cullen 1995), or because they show high growth rates under low light conditions due to the presence of phycoerythrin (Gervais et al. 1997; Camacho et al. 2001). Our results, however, should be interpreted with caution as the subset of lakes where spectroﬂuorometer data were available represented a geographically constrained subset of our entire dataset (31 of the 37 lakes were located in southeastern Canada). Future studies that examine species composition of the DCM across a broad range of lakes may provide more insights into the generality of the patterns observed in our data and the relative importance of different mechanism of DCM formation (e.g., behavioral aggregations vs. in situ growth).

Additional considerations While care was taken to collect high-quality, representa- tive data from across our study systems, some fundamental data collection challenges warrant consideration. Approxi- mately half of the light attenuation data for this study was derived from Secchi depth observations. Differences in attenuation controlled by particulate scattering vs. DOC absorp- tion may lead to variation in 1% PAR depth not explained by Secchi depth (Koenings and Edmundson 1991). We were not able to comprehensively compare differences in the estimates of 1% attenuation depths between radiometer and Sec- chi readings because only six lakes in our dataset had both radiometer and Secchi readings. Within those six lakes, we found no consistent pattern in over- or underestimation of 1% PAR depths based on values derived from Secchi vs. radiometer-based measurements. The difference in 1% PAR depth estimates between the Secchi vs. radiometer-based methods within each lake varied by an average of 20% (6 10% SD). Despite the added variability in 1% PAR depth estimates that was introduced in our data, 1% PAR depth was by far the most important explanatory variable for DCM depth, suggesting that the methods of light measurements were sufficient to observe this important pattern. Broad-scale use of optical profiling techniques over Secchi disks will improve our understanding of the relationship between DCM depth and the underwater light environment by providing estimates of irradiance or daily radiant exposure throughout the water column, spectral composition at the depth of the DCM, and more accurate estimates of light attenuation. To our knowledge we are the first to incorporate an exponential power distribution into a model to characterize ChlF profiles (Eq. 1). We found that the additional parameter improved (based on higher R2) the characterization of the ChlF profiles compared with a curve fit using a Gaussian distribution. Further, visual inspection did not indicate the model Fig. 7. Partial dependency plots for the top three most important pre- overfit profiles, rather, the model was more versatile and better dictors from the random forest model, where DCM thickness was the fit the range of DCM shapes observed (Fig. 2c–f). Using the response variable; (a–c) are in descending order of importance; all else exponential power distribution allowed us to expand the as in Fig. 6.

641 Leach et al. Patterns and drivers of DCM structure across lakes

broad gradients of lake size, maximum depth, and transparency. For example, small decreases in the 1% PAR depth may cause a more dramatic reduction in the DCM depth in high transparency lakes but have a much smaller inﬂuence in low transparency lakes. The diversity of lakes in our dataset demonstrates that DCMs occur across many different types of lakes, not just clear oligotrophic lakes. Future ecosystem studies may need to consider physical, chemical, and biological processes that occur in deeper parts of the water column, as well as in the surface mixed layer of many lake types. Our study demonstrates that recent advances in high-resolution proﬁling, in combina- tion with collaborative, data-sharing networks such as GLEON, provide excellent opportunities to improve the understanding of important ecological processes by allowing for studies that encompass a large number of diverse lakes.

Author contribution statement All authors contributed to the conception of the work as part of the Global Lake Ecological Observatory Network (GLEON) meeting in Orford, Quebec, Canada (2014) and/or subsequent conference calls with discussions led by BEB, CCC, Fig. 8. Average buoyancy frequency (s21) in the depth range of the and THL. After the lead author, authors are listed in two tiers DCM vs. the thickness of the DCM. Note the high variability in DCM according to contribution. THL, BEB, CCC, PP, KCR, and YH thickness when buoyancy frequency is low, but that the thickness is less contributed substantially to discussions regarding the analyti- variable and thinner at high buoyancy frequency values. cal approaches and conceptual framing of this project. The authors after these initial six are listed alphabetically and con- breadth and diversity of lakes that we were able to include in tributed to interpretation of the results and the discussion. our study. For the subset of lakes where R2 >5 0.8 from the THL led the writing of the manuscript, and conducted all sta- ChlF curve fitting procedure, the median value of the shape tistical analyses. PP estimated all metrics associated with buoy- parameter was 1.7 (mean 5 8.0 (3.3 standard error), 1st–3rd ancy frequency. BEB, CCC, ID, HPG, THL, KCR, JAR, JDS, DS, quartile 5 1.0–2.6; note that the mean is driven by a small and PV contributed data. All authors critically revised the number of large values) indicating that the DCMs in our data- manuscript for intellectual content and approved of the final set were similar in shape to a Gaussian distribution but tended version of the manuscript for publication. to have heavier tails. Characterizations of DCMs in future studies may be improved by using the exponential power dis- References tribution with a shape parameter that is less than two. Abbott, M. R., K. L. Denman, T. M. Powell, P. J. Richerson, R. C. Richards, and C. R. Goldman. 1984. Mixing and the Conclusions dynamics of the deep chlorophyll maximum in Lake Our results show that the depth of light attenuation, lake Tahoe. Limnol. Oceanogr. 29: 862–878. doi:10.4319/ size, and maximum lake depth explain a substantial amount of lo.1984.29.4.0862 variation in the DCM depth and thickness. Light attenuation Abell, R., and others. 2008. Freshwater ecoregions of the was a more important predictor of DCM depth than was ther- world: A new map of biogeographic units for freshwater mal stratification, while DCM thickness was best predicted by biodiversity conservation. Bioscience 58: 403–414. doi: lake size and maximum depth. Long-term increasing or decreas- 10.1641/B580507 ing trends in water clarity (Lottig et al. 2014; Williamson et al. Alldredge, A. L., and others. 2002. Occurrence and mecha- 2015) will alter the depths of light attenuation (Williamson nisms of formation of a dramatic thin layer of marine et al. 1996b) and thermal stratification (Read and Rose 2013) snow in a shallow Pacific fjord. Mar. Ecol. Prog. Ser. 233: with important consequences for DCM structure. In an impor- 1–12. doi:10.3354/meps233001 tant extension of previous studies, our analysis also suggests Archer, K. J., and R. V. Kimes. 2008. Empirical characteriza- that changing environmental conditions (e.g., eutrophication, tion of random forest variable importance measures. oligotrophication, brownification, changing thermal structure) Comput. Stat. Data Anal. 52: 2249–2260. doi:10.1016/ may affect the depth and thickness of DCMs differently across j.csda.2007.08.015

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Verti- We thank Erin Overholt for assistance with processing and manage- ment of data from lakes in Beartooth Mountains, Canadian Rockies, Gla- cal distribution of phytoplankton communities in open cier National Park, Poconos Mountains and Sierra Nevada. Data from ocean: An assessment based on surface chlorophyll. J. lakes Annecy, Leman, and Bourget were collected by OLA observatory, Geophys. Res. 111: C08005. doi:10.1029/2005JC003207 with thanks to INRA Thonon-les-Bains, CISALB, CIPEL, SILA, and the Varela, R. A., A. Cruzado, J. Tintore, and E. Garda Ladona. SOERE OLA-IS developed by ORE Eco-Informatique group. Data from 1992. Modelling the deep-chlorophyll maximum: A cou- Lake Stechlin were collected by the MIBI group with special thanks to Elke Mach, IGB and the Leibniz Association for financial support. For the pled physical-biological approach. J. Mar. Res. 50: 441– majority of the Quebec, Canada lakes, we acknowledge Maria Lorena 463. doi:10.1357/002224092784797638 Longhi, Allain Barnett, Fonds de Recherche du Quebec – Nature et Tech- Varela, R. A., A. Cruzado, and J. Tintore. 1994. A simulation nologie (FRQNT) and the Natural Sciences and Engineering Research analysis of various biological and physical factors Council of Canada (NSERC) to BEB. KCR acknowledges funding support influencing the deep-chlorophyll maximum structure in from NSF grant EF 1638704. JAR acknowledges funding from the Ontario Ministry of the Environment and Climate Change and the Inter-American oligotrophic areas. J. Mar. Syst. 5: 143–157. doi:10.1016/ Institute for Global Change Research (Grant CRN3038). Thanks to Craig 0924-7963(94)90028-0 Williamson, Melany Fisk, A. John Bailer, Janet Fischer and Michael Vanni Villareal, T. A., S. Woods, J. K. Moore, and K. Culver- for thoughtful feedback on this manuscript and special thanks to Luke Rymsza. 1996. Vertical migration of Rhizosolenia mats Winslow for his helpful advice with the data analysis and comments on drafts of this manuscript. Finally, we would like to thank John Cullen and and their significance to NO3- fluxes in the Central an anonymous reviewer for their helpful feedback that improved this Pacific gyre. J. Plankton Res. 18: 1103–1121. doi:10.1093/ manuscript. Our work was made possible by coauthors’ participation in plankt/18.7.1103 the Global Lake Ecological Observatory Network (GLEON). Weathers, K., and others. 2013. The Global Lake Ecological Conflict of Interest Observatory Network (GLEON): The evolution of grass- None declared. roots network science. Limnol. Oceanogr. Bull. 22: 71–73. doi:10.1002/lob.201322369 Submitted 30 January 2017 Weston, K., L. Fernand, D. K. Mills, R. Delahunty, and J. Revised 31 May 2017 Brown. 2005. Primary production in the deep chlorophyll Accepted 18 July 2017 maximum of the central North Sea. J. Plankton Res. 27: 909–922. doi:10.1093/plankt/fbi064 Associate editor: Francisco Rueda

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